I think you have just described my daughter!!!! I have been trying for a while now to potty train my daughter who is also 3 (turned in Jan). She had no interest in even sitting on the potty. I decided one day to try the reward system like one of the other suggestions. I made a bunch of squares and at the end of about 6 squares I wrote the word reward and explained to her that if she goes pee pee on the potty she will get 1 sticker, and two for poo poo. If she reaches the reward square we will go buy her a prize. For her it was a "journal" that she really wanted so that she could scribble in it. It worked to get her interested in it, but still she would decide when she wanted to go on it and it wasn't as frquent as I hoped. So after reading some posts on cafe mom, I decided that I would be brave and just slap underwear on her every morning and deal with whatever came my way. It has worked to a point. She does good most of the day, but still has at least one accident a day, and she's been in underwear for over 2 weeks. I know its very frustrating, but every child is different. There is no cookie cutter mold that fits every child. My daughter is incredibly bright, but has always been a step behind with some physical developments, like rolling over, sitting up, walking, ect. She was talking in full sentences, counting to 20 and singing the alphabet by her 2nd birthday. So hang in there and keep trying, but don't push her because she will just regress.